Block #62,938

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 10:22:16 PM · Difficulty 8.9778 · 6,728,816 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

7a93d9bc31abb57ead1450fc87246056f86e219150b67842df0aa81945515852

View on Chainz ↗

Height

#62,938

Difficulty

8.977815

Transactions

Size

873 B

Version

Bits

08fa521c

Nonce

376

Timestamp

7/18/2013, 10:22:16 PM

Confirmations

6,728,816

Merkle Root

b43fa182214b2de743344475ea15f1e274db436ce3a96d10e301ca0b27795a7a

Transactions (2)

Coinbasef69eae942a0992…15e28c4dac341b

1 in → 1 out12.4000 XPM109 B

ATHwZN7q…mASXN9sQ

c051948228d2cc…62ef4292da5c3b

4 in → 2 out1.2123 XPM670 B

AcDmKYR3…brUcutjF AL2QJjTa…2a4dBYh5

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.961 × 10¹⁰⁵(106-digit number)

19613391280742701323…11173161861548465919

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.961 × 10¹⁰⁵(106-digit number)

19613391280742701323…11173161861548465919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.961 × 10¹⁰⁵(106-digit number)

19613391280742701323…11173161861548465921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.922 × 10¹⁰⁵(106-digit number)

39226782561485402647…22346323723096931839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.922 × 10¹⁰⁵(106-digit number)

39226782561485402647…22346323723096931841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

7.845 × 10¹⁰⁵(106-digit number)

78453565122970805294…44692647446193863679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.845 × 10¹⁰⁵(106-digit number)

78453565122970805294…44692647446193863681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.569 × 10¹⁰⁶(107-digit number)

15690713024594161058…89385294892387727359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.569 × 10¹⁰⁶(107-digit number)

15690713024594161058…89385294892387727361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.138 × 10¹⁰⁶(107-digit number)

31381426049188322117…78770589784775454719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer